Recent reports suggested that the pair had been arguing over the former glamour model's 'obsession' with her ex-husband Peter Andre.
"I appreciate to some it may seem strange that I should feel aggrieved by aspects of the recent press coverage of my marriage to Alex," she wrote on her official website. "Some will feel that adverse stories are the price I have to pay for living my life so openly. However, I need to respond to a recent series of stories that Alex and I are on the verge of, or have, split."
Price stated that the original source of the stories was a Sunday newspaper, which was told that the claims were false before publication. She claimed that follow-up reports in daily newspapers were also informed about the accuracy of the sources.
"Either these publications have a source that is taking them for a ride or they don't care if they mislead their readers," she added. "Constantly publishing these fabrications despite being told they are just that is hurtful and harassing."
She informed fans that her lawyers were already dealing with the stories, but said that she wanted to respond herself.
In a series of bullet-pointed denials, Price said: "Alex and I are not constantly arguing."
She rebutted reports that she had "run away to Portugal" following more rows with Reid and confirmed that he had not joined the family because he is training for his upcoming fight.
In her next point, she wrote: "Alex has not left me, threatened to leave me or confronted me about my ex-husband, Amir Khan or any other man. Alex is secure in the knowledge that I love him as I am in the knowledge that he loves me."
Discussing reports which claimed that she was still in love with Andre, she added: "Peter Andre is the father of two of my children. I respect him and have contact with him in that capacity. I do not wish to get back with Peter and Peter does not wish to get back with me. We have both moved on with our lives."
Finally, she confirmed once again that she was not pregnant.
"I hope this puts an end to the false stories that are being published," she said.